Resonant Inelastic X-ray Scattering (RIXS)
 is an X-ray in, X-ray out technique that enables one to study the 
dispersion of excitations in solids. In this thesis, we investigated how
 various elementary excitations of transition metal oxides show up in 
RIXS spectra.

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Resonant Inelastic X-ray Scattering Studies of Elementary Excitations

We report a resonant inelastic x-ray scattering study of the dispersion relations of charge-transfer excitations in insulating La(2)CuO(4).. These data reveal two peaks, both of which show two-dimensional characteristics. The lowest energy excitation has a gap energy of approximately 2.2 eV at the zone enter, and a dispersion of approximately 1 eV. The spectral weight of this mode becomes dramatically smaller around (pi, pi). The second peak shows a smaller dispersion ( approximately 0.5 eV) with a zone-center energy of approximately 3.9 eV. We argue that these are both highly dispersive exciton modes damped by the presence of the electron-hole continuum.

Resonant inelastic x-ray scattering study of charge excitations in La(2)CuO(4).

The density-matrix renormalization-group (DMRG) method is used to investigate optical excitations in the Mott insulating phase of a one-dimensional extended Hubbard model. The linear optical conductivity is calculated using the dynamical DMRG method and the nature of the lowest optically excited states is investigated using a symmetrized DMRG approach. The numerical calculations agree perfectly with field-theoretical predictions for a small Mott gap and analytical results for a large Mott gap obtained with a strong-coupling analysis. It is shown that four types of optical excitations exist in this Mott insulator: pairs of unbound charge excitations, excitons, excitonic strings, and charge-density-wave (CDW) droplets. Each type of excitation dominates the low-energy optical spectrum in some region of the interaction parameter space and corresponds to distinct spectral features: a continuum starting at the Mott gap (unbound charge excitations), a single peak or several isolated peaks below the Mott gap (excitons and excitonic strings, respectively), and a continuum below the Mott gap (CDW droplets).

https://arxiv.org/pdf/cond-mat/0208480.pdf

Optical excitations in a one-dimensional Mott insulator

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached We propose that inelastic x-ray scattering be used to detect this mode Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition

/pdf/dynamical-properties-of-a-strongly-correlated-model-for-1bvvf6qlf6.pdf

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

In indirect resonant inelastic x-ray scattering RIXS an intermediate state is created with a core-hole that has an ultrashort lifetime. The core-hole potential therefore acts as a femtosecond pulse on the valence electrons. We show that this fact can be exploited to integrate out the intermediate states from the expression for the scattering cross section. By doing so we obtain an effective scattering cross section that only contains the initial and final scattering states. This effective cross section turns out to be a linear combination of the charge response function Sq, and the dynamic longitudinal spin density correlation function, both with a resonant prefactor. This result is asymptotically exact for both strong and weak local core-hole potentials and ultrashort lifetimes. The resonant scattering prefactor is shown to be weakly temperature dependent. We also derive a sum rule for the total scattering intensity and generalize the results to multiband systems. One of the remarkable outcomes is that one can change the relative charge and spin contribution to the inelastic spectral weight by varying the incident photon energy.

Ultrashort Lifetime Expansion for Indirect Resonant Inelastic X-ray Scattering

We report momentum-resolved charge excitations in a one-dimensional (ID) Mott insulator studied using high resolution inelastic x-ray scattering over the entire Brillouin zone for the first time. Excitations at the insulating gap edge are found to be highly dispersive (momentum dependent) compared to excitations observed in two-dimensional Mott insulators. The observed dispersion in ID cuprates (SrCuO 2 and Sr 2 CuO 3 ) is consistent with charge excitations involving holons which is unique to spin-½ quantum chain systems. These results point to the potential utility of momentum-resolved inelastic x-ray scattering in providing valuable information about electronic structure of strongly correlated insulators.

Sinha Sk

Papers

Momentum-resolved charge excitations in a prototype one-dimensional mott insulator.